MAI0115
Optimal control, brief introductory course
Number of credits: 1 hp
Examiner: Gunnar Aronsson
Course literature: J. Macki, A. Strauss: Introduction to optimal control theory, Springer Verlag 1995. Lawrence C. Evans: An introduction to mathematical optimal control theory; Version 0.2. University of California, Berkeley. Lecture notes, available from Evans' home page.
Course contents:
- Some mathematical basics, like: Caratheodory solution concept for ODE; Mayer problem, Bolza problem; Big-bang principle (without proof); variational system, adjoint system; Time-optimal problems; "Spike variations".
- First cases of a Boltyanski-Pontryagin maximum principle; Adjoint response, transversality condition; Adjoint vector seen as shadow values; Hamiltonian function; Economic interpretation of the maximum principle; Hamilton-Jacobi-Bellman equation.
- Examples, most of them from economics.
- Deriving a maximum principle for problems with fixed time and fixed end-point. A more difficult Bolza problem. Basic perturbation formula. A covering property of continuous mappings; A B-P maximum principle.
Organisation: 10 teorilektioner + 4 lektioner för lösning av övningsuppgifter.
Examination: Tillräcklig närvaro under kursen + deltagande i problemlösning.
Prerequisites: Flevariabelanalys + (helst) någon kunskap om ordinära differentialekvationer.
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Last updated: 2022-11-15